Question

If the mass is of 10 Kg, find the natural frequency in Hz of the free longitudinal vibrations. The displacement is 0.01mm.

(a) 44.14

(b) 49.85

(c) 43.43

(d) 46.34

I had been asked this question in unit test.

The question is from Natural Frequency of Free Longitudinal Vibrations in portion Longitudinal and Transverse Vibrations of Machine Dynamics

Answer 1

The correct option is (b) 49.85

Easy explanation: We know that the natural Frequency of Free Longitudinal Vibration is given by the equation

f = 0.4985/\(\sqrt{s}\)

where s is the displacement of the spring.

substituting the given values we get

f=49.85 Hz

It is to be noted that mass has no effect on the natural frequency as it only depends on the displacement.